e_err.cc

#include <algorithm>
#include <cmath>
#include <iomanip>
#include <iostream>
using namespace std;

#define STR_(X)  (#X)
#define STR(X)  (STR_(X))
#define ACTUAL  2.71828182845904523536028747135266249776

template<class Int, class Real=long double>
struct E {
  void operator()() const {
    Real actual = ACTUAL;
    Real e = 1;
    Int fact = 1;
    int i = 1;

    while (fact > 0) {
      fact *= i;
      e += 1.0 / fact;
      ++i;
    }

    Real error = abs(actual - e);
    Real log_error = -(1/log(10) * log(error));
    Real sqrt_log_error = sqrt(log_error);
    const int P = 40;
    cout
      << setprecision(P)
      //<< setw(P) << i << "\titerations in "
      //<< (t2-t1).count() << "ns\n"
      //<< e << "\tcomputed\n"
      //<< STR(ACTUAL) << "\tactual_str\n"
      //<< actual << "\tactual\n"
      //<< setprecision(P-4) << error << "\terror\n"
      //<< setprecision(P) << log_error << "\t-log10(error)\n"
      //<< sqrt_log_error << "\tsqrt(-log10(error)\n"
      << setw(P) << round(sqrt_log_error) << "\tround(sqrt(-log10(error)))\n"
      //<< setw(P) << sizeof(Int) << "\tsizeof(Int)\n"
      << "\n";
  }
};

int main() {
  E<char>()();
  E<short>()();
  E<int>()();
  E<long>()();
  return 0;
}